Question

A real image of an object is formed at a distance of $20cm$ from a lens. On putting another lens in contact with it, the image is shifted $10cm$ towards the combination. The power of the lens is

• A. $2D$
• B. $5D$
• C. $6D$
• D. $10D$

Answer 1

Answer: (B)

As image formed is real, therefore lens must be convex, $v=20cm$. Let $f_1$, be focal length for this lens.
$\therefore \frac{1}{f_1}=\frac{1}{v}-\frac{1}{u}=\frac{1}{20}-\frac{1}{u}$
After placing it in contact with another lens, the image shifted to $10cm$ towards the combination
i.e., $v=(20-10)cm=10cm$
$\therefore \frac{1}{10}-\frac{1}{u}=\frac{1}{f_1}+\frac{1}{f_2}=\left(\frac{1}{20}-\frac{1}{u}\right)+\frac{1}{f_2}$
$\Rightarrow f_2=20cm$
$\therefore P=\frac{100}{20}{m}^{-1}=5D$